A Product of the Ground-Water Resource Program

Documentation of the Streamflow-Routing (SFR2) Package to Include Unsaturated
Flow Beneath Streams—A Modification to SFR1

By Richard G. Niswonger and David E. Prudic

Abstract

Many streams in the United States, especially those in semiarid regions, have reaches that are hydraulically disconnected from underlying aquifers. Ground-water withdrawals have decreased water levels in valley aquifers beneath streams, increasing the occurrence of disconnected streams and aquifers. The U.S. Geological Survey modular ground-water model (MODFLOW-2000) can be used to model these interactions using the Streamflow-Routing (SFR1) Package. However, the approach does not consider unsaturated flow between streams and aquifers and may not give realistic results in areas with significantly deep unsaturated zones. This documentation describes a method for extending the capabilities of MODFLOW-2000 by incorporating the ability to simulate unsaturated flow beneath streams.

A kinematic-wave approximation to Richards’ equation was solved by the method of characteristics to simulate unsaturated flow beneath streams in SFR1. This new package, called SFR2, includes all the capabilities of SFR1 and is designed to be used with MODFLOW-2000. Unlike SFR1, seepage loss from the stream may be restricted by the hydraulic conductivity of the unsaturated zone. Unsaturated flow is simulated independently of saturated flow within each model cell corresponding to a stream reach whenever the water table (head in MODFLOW) is below the elevation of the streambed. The relation between unsaturated hydraulic conductivity and water content is defined by the Brooks-Corey function. Unsaturated flow variables specified in SFR2 include saturated and initial water contents; saturated vertical hydraulic conductivity; and the Brooks-Corey exponent. These variables are defined independently for each stream reach. Unsaturated flow in SFR2 was compared to the U.S. Geological Survey’s Variably Saturated Two-Dimensional Flow and Transport (VS2DT) Model for two test simulations. For both test simulations, results of the two models were in good agreement with respect to the magnitude and downward progression of a wetting front through an unsaturated column. A third hypothetical simulation is presented that includes interaction between a stream and aquifer separated by an unsaturated zone. This simulation is included to demonstrate the utility of unsaturated flow in SFR2 with MODFLOW-2000. This report includes a description of the data input requirements for simulating unsaturated flow in SFR2.